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Volumn 2, Issue 4, 2009, Pages 275-365

Dimension reduction: A guided tour

Author keywords

[No Author keywords available]

Indexed keywords

CANONICAL CORRELATION ANALYSIS; CORRELATION DIMENSIONS; DATA SETS; DIMENSION REDUCTION; FISHER DISCRIMINANT ANALYSIS; INTRINSIC DIMENSIONS; KERNEL PCA; LAPLACIAN EIGENMAPS; LOCALLY LINEAR EMBEDDING; M METHOD; MULTI-DIMENSIONAL SCALING; PROBABILISTIC PCA; PROJECTION PURSUITS; PROJECTIVE METHODS; SPECTRAL CLUSTERING; SUFFICIENT DIMENSION REDUCTION;

EID: 77958497920     PISSN: 19358237     EISSN: 19358245     Source Type: Journal    
DOI: 10.1561/2200000002     Document Type: Article
Times cited : (200)

References (100)
  • 2
    • 0000874557 scopus 로고
    • Theoretical foundations of the potential function method in pattern recognition learning
    • M. A. Aizerman, E. M. Braverman, and L. I. Rozoner, "Theoretical foundations of the potential function method in pattern recognition learning," Automation and Remote Control, vol. 25, pp. 821-837, 1964.
    • (1964) Automation and Remote Control , vol.25 , pp. 821-837
    • Aizerman, M.A.1    Braverman, E.M.2    Rozoner, L.I.3
  • 6
  • 8
    • 0042378381 scopus 로고    scopus 로고
    • Laplacian eigenmaps for dimensionality reduction and data representation
    • M. Belkin and P. Niyogi, "Laplacian Eigenmaps for dimensionality reduction and data representation," Neural Computation, vol. 15, pp. 1373-1396, 2003.
    • (2003) Neural Computation , vol.15 , pp. 1373-1396
    • Belkin, M.1    Niyogi, P.2
  • 15
    • 27144489164 scopus 로고    scopus 로고
    • A tutorial on support vector machines for pattern recognition
    • C. J. C. Burges, "A tutorial on support vector machines for pattern recognition," Data Mining and Knowledge Discovery, vol. 2, pp. 121-167, 1998.
    • (1998) Data Mining and Knowledge Discovery , vol.2 , pp. 121-167
    • Burges, C.J.C.1
  • 16
    • 35048900986 scopus 로고    scopus 로고
    • Some notes on applied mathematics for machine learning
    • (O. Bousquet, U. von Luxburg, and G. Rätsch, eds.), Springer Lecture Notes in Artificial Intelligence
    • C. J. C. Burges, "Some notes on applied mathematics for machine learning," in Advanced Lectures on Machine Learning, (O. Bousquet, U. von Luxburg, and G. Rätsch, eds.), pp. 21-40, Springer Lecture Notes in Artificial Intelligence, 2004.
    • (2004) Advanced Lectures on Machine Learning , pp. 21-40
    • Burges, C.J.C.1
  • 28
    • 0042024221 scopus 로고    scopus 로고
    • Factor analysis
    • Cornell University
    • R. B. Darlington, "Factor analysis," Technical report, Cornell University, http://comp9.psych.cornell.edu/Darlington/factor.htm, 1997.
    • (1997) Technical Report
    • Darlington, R.B.1
  • 29
    • 85156202169 scopus 로고    scopus 로고
    • Global versus local methods in nonlinear dimensionality reduction
    • MIT Press
    • V. De Silva and J. B. Tenenbaum, "Global versus local methods in nonlinear dimensionality reduction," Advances in Neural Information Processing Systems, vol. 15, pp. 705-712, MIT Press, 2002.
    • (2002) Advances in Neural Information Processing Systems , vol.15 , pp. 705-712
    • De Silva, V.1    Tenenbaum, J.B.2
  • 31
    • 0001493668 scopus 로고
    • Asymptotics of graphical projection pursuit
    • P. Diaconis and D. Freedman, "Asymptotics of graphical projection pursuit," Annals of Statistics, vol. 12, pp. 793-815, 1984.
    • (1984) Annals of Statistics , vol.12 , pp. 793-815
    • Diaconis, P.1    Freedman, D.2
  • 37
    • 0016102310 scopus 로고
    • A projection pursuit algorithm for exploratory data analysis
    • J. H. Friedman and J. W. Tukey, "A projection pursuit algorithm for exploratory data analysis," IEEE Transactions on Computers, vol. 23, pp. 881-890, 1974.
    • (1974) IEEE Transactions on Computers , vol.23 , pp. 881-890
    • Friedman, J.H.1    Tukey, J.W.2
  • 38
    • 68649121147 scopus 로고    scopus 로고
    • Kernel dimension reduction in regression
    • K. Fukumizu, F. R. Bach, and M. I. Jordan, "Kernel dimension reduction in regression," Annals of Statistics, vol. 37, pp. 1871-1905, 2009.
    • (2009) Annals of Statistics , vol.37 , pp. 1871-1905
    • Fukumizu, K.1    Bach, F.R.2    Jordan, M.I.3
  • 43
    • 40749093037 scopus 로고
    • Measuring the strangeness of strange attractors
    • P. Grassberger and I. Procaccia, "Measuring the strangeness of strange attractors," Physica, vol. 9D, pp. 189-208, 1983.
    • (1983) Physica , vol.D , pp. 189-208
    • Grassberger, P.1    Procaccia, I.2
  • 47
    • 10044285992 scopus 로고    scopus 로고
    • Canonical correlation analysis: An overview with application to learning methods
    • D. R. Hardoon, S. Szedmak, and J. Shawe-Taylor, "Canonical correlation analysis: An overview with application to learning methods," Neural Computation, vol. 12, pp. 2639-2664, 2004.
    • (2004) Neural Computation , vol.12 , pp. 2639-2664
    • Hardoon, D.R.1    Szedmak, S.2    Shawe-Taylor, J.3
  • 49
    • 0000379660 scopus 로고
    • Computing the nearest symmetric positive semidefinite matrix
    • N. J. Higham, "Computing the nearest symmetric positive semidefinite matrix," Linear Algebra and its Applications, vol. 103, pp. 103-118, 1988.
    • (1988) Linear Algebra and Its Applications , vol.103 , pp. 103-118
    • Higham, N.J.1
  • 50
    • 0013344078 scopus 로고    scopus 로고
    • Training products of experts by minimizing contrastive divergence
    • G. E. Hinton, "Training products of experts by minimizing contrastive divergence," Neural Computation, vol. 14, pp. 1771-1800, 2002.
    • (2002) Neural Computation , vol.14 , pp. 1771-1800
    • Hinton, G.E.1
  • 51
    • 33745805403 scopus 로고    scopus 로고
    • A fast learning algorithm for deep belief nets
    • G. E. Hinton, S. Osindero, and Y. Teh, "A fast learning algorithm for deep belief nets," Neural Computation, vol. 7, pp. 1527-1554, 2006.
    • (2006) Neural Computation , vol.7 , pp. 1527-1554
    • Hinton, G.E.1    Osindero, S.2    Teh, Y.3
  • 53
    • 33746600649 scopus 로고    scopus 로고
    • Reducing the dimensionality of data with neural networks
    • G. E. Hinton and R. Salakhutdinov, "Reducing the dimensionality of data with neural networks," Science, vol. 313, pp. 504-507, 2007.
    • (2007) Science , vol.313 , pp. 504-507
    • Hinton, G.E.1    Salakhutdinov, R.2
  • 55
    • 0000107975 scopus 로고
    • Relations between two sets of variates
    • H. Hotelling, "Relations between two sets of variates," Biometrika, vol. 28, pp. 321-377, 1936.
    • (1936) Biometrika , vol.28 , pp. 321-377
    • Hotelling, H.1
  • 56
    • 65349144349 scopus 로고    scopus 로고
    • An RKHS formulation of the inverse regression dimension-reduction problem
    • T. Hsing and H. Ren, "An RKHS formulation of the inverse regression dimension-reduction problem," Annals of Statistics, vol. 37, pp. 726-755, 2009.
    • (2009) Annals of Statistics , vol.37 , pp. 726-755
    • Hsing, T.1    Ren, H.2
  • 57
    • 0000263797 scopus 로고
    • Projection pursuit
    • P. J. Huber, "Projection pursuit," Annals of Statistics, vol. 13, pp. 435-475, 1985.
    • (1985) Annals of Statistics , vol.13 , pp. 435-475
    • Huber, P.J.1
  • 63
    • 26444566340 scopus 로고    scopus 로고
    • Contour regression: A general approach to dimension reduction
    • B. Li, H. Zha, and F. Chiaromonte, "Contour regression: A general approach to dimension reduction," The Annals of Statistics, vol. 33, pp. 1580-1616, 2005.
    • (2005) The Annals of Statistics , vol.33 , pp. 1580-1616
    • Li, B.1    Zha, H.2    Chiaromonte, F.3
  • 64
    • 84945116550 scopus 로고
    • Sliced Inverse Regression for dimension reduction
    • C.-K. Li, "Sliced Inverse Regression for dimension reduction," Journal of the American Statistical Association, vol. 86, pp. 316-327, 1991.
    • (1991) Journal of the American Statistical Association , vol.86 , pp. 316-327
    • Li, C.-K.1
  • 65
    • 84950441056 scopus 로고
    • On Principal Hessian Directions for data visualization and dimension reduction: Another application of Stein's lemma
    • C.-K. Li, "On Principal Hessian Directions for data visualization and dimension reduction: Another application of Stein's lemma," Journal of the American Statistical Association, vol. 87, pp. 1025-1039, 1992.
    • (1992) Journal of the American Statistical Association , vol.87 , pp. 1025-1039
    • Li, C.-K.1
  • 75
    • 0034704222 scopus 로고    scopus 로고
    • Nonlinear dimensionality reduction by locally linear embedding
    • S. T. Roweis and L. K. Saul, "Nonlinear dimensionality reduction by locally linear embedding," Science, vol. 290, pp. 2323-2326, 2000.
    • (2000) Science , vol.290 , pp. 2323-2326
    • Roweis, S.T.1    Saul, L.K.2
  • 76
    • 2342517502 scopus 로고    scopus 로고
    • Think globally, fit locally: Unsupervised learning of low dimensional manifolds
    • L. K. Saul and S. T. Roweis, "Think globally, fit locally: Unsupervised learning of low dimensional manifolds," Journal of Machine Learning Research, vol. 4, pp. 119-155.
    • Journal of Machine Learning Research , vol.4 , pp. 119-155
    • Saul, L.K.1    Roweis, S.T.2
  • 77
    • 33750733400 scopus 로고    scopus 로고
    • Spectral methods for dimensionality reduction
    • (O. Chapelle, B. Schölkopf, and A. Zien, eds., MIT Press
    • L. K. Saul, K. Q. Weinberger, J. H. Ham, F. Sha, and D. D. Lee, "Spectral methods for dimensionality reduction," in Semisupervised Learning, (O. Chapelle, B. Schölkopf, and A. Zien, eds.), pp. 293-308, MIT Press, 2006.
    • (2006) Semisupervised Learning , pp. 293-308
    • Saul, L.K.1    Weinberger, K.Q.2    Ham, J.H.3    Sha, F.4    Lee, D.D.5
  • 78
    • 0001203499 scopus 로고
    • Remarks to Maurice Frechet's article Sur la définition axiomatique d'une classe d'espace distancíes vectoriellement applicable sur l'espace de hilbert
    • I. J. Schoenberg, "Remarks to Maurice Frechet's article Sur la définition axiomatique d'une classe d'espace distancíes vectoriellement applicable sur l'espace de hilbert," Annals of Mathematics, vol. 36, pp. 724-732, 1935.
    • (1935) Annals of Mathematics , vol.36 , pp. 724-732
    • Schoenberg, I.J.1
  • 81
    • 0347243182 scopus 로고    scopus 로고
    • Nonlinear component analysis as a kernel eigenvalue problem
    • B. Schölkopf, A. Smola, and K.-R. Muller, "Nonlinear component analysis as a kernel eigenvalue problem," Neural Computation, vol. 10, pp. 1299-1319, 1998.
    • (1998) Neural Computation , vol.10 , pp. 1299-1319
    • Schölkopf, B.1    Smola, A.2    Muller, K.-R.3
  • 83
    • 0000600340 scopus 로고
    • General intelligence objectively determined and measured
    • C. E. Spearman, "'General intelligence' objectively determined and measured," American Journal of Psychology, vol. 5, pp. 201-293, 1904.
    • (1904) American Journal of Psychology , vol.5 , pp. 201-293
    • Spearman, C.E.1
  • 84
    • 0010786475 scopus 로고    scopus 로고
    • On the influence of the kernel on the consistency of support vector machines
    • I. Steinwart, "On the influence of the kernel on the consistency of support vector machines," Journal of Machine Learning Research, vol. 37, pp. 726- 755, 2001.
    • (2001) Journal of Machine Learning Research , vol.37 , pp. 726-755
    • Steinwart, I.1
  • 85
    • 0000439527 scopus 로고
    • Optimal global rates of convergence for nonparametric regression
    • C. J. Stone, "Optimal global rates of convergence for nonparametric regression," Annals of Statistics, vol. 10, pp. 1040-1053, 1982.
    • (1982) Annals of Statistics , vol.10 , pp. 1040-1053
    • Stone, C.J.1
  • 86
    • 33746329499 scopus 로고    scopus 로고
    • The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem
    • J. Sun, S. Boyd, L. Xiao, and P. Diaconis, "The fastest mixing Markov process on a graph and a connection to a maximum variance unfolding problem," Society for Industrial and Applied Mathematics (SIAM) Review, vol. 48, pp. 681-699, 2006.
    • (2006) Society for Industrial and Applied Mathematics (SIAM) Review , vol.48 , pp. 681-699
    • Sun, J.1    Boyd, S.2    Xiao, L.3    Diaconis, P.4
  • 88
    • 0033556788 scopus 로고    scopus 로고
    • Mixtures of probabilistic principal component analyzers
    • M. E. Tipping and C. M. Bishop, "Mixtures of probabilistic principal component analyzers," Neural Computation, vol. 11, pp. 443-482, 1999.
    • (1999) Neural Computation , vol.11 , pp. 443-482
    • Tipping, M.E.1    Bishop, C.M.2
  • 95
    • 34548583274 scopus 로고    scopus 로고
    • A tutorial on spectral clustering
    • U. von Luxburg, "A tutorial on spectral clustering," Statistics and Computing, vol. 17, no. 4, pp. 395-416, 2007.
    • (2007) Statistics and Computing , vol.17 , Issue.4 , pp. 395-416
    • Von Luxburg, U.1
  • 98
    • 84898939890 scopus 로고    scopus 로고
    • On a connection between kernel PCA and metric multidimensional scaling
    • MIT Press
    • C. K. I. Williams, "On a connection between kernel PCA and metric multidimensional scaling," Advances in Neural Information Processing Systems, vol. 13, pp. 675-681, MIT Press, 2001.
    • (2001) Advances in Neural Information Processing Systems , vol.13 , pp. 675-681
    • Williams, C.K.I.1
  • 100
    • 59349084916 scopus 로고    scopus 로고
    • Multiway spectral clustering: A margin-based perspective
    • Z. Zhang and M. I. Jordan, "Multiway spectral clustering: A margin-based perspective," Statistical Science, vol. 23, pp. 383-403, 2008.
    • (2008) Statistical Science , vol.23 , pp. 383-403
    • Zhang, Z.1    Jordan, M.I.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.